Is the common law marriage legally bound by filing my taxes using my husband's last name on them?
Your question is not a tax question---it is a legal question. Consult an attorney.
https://www.divorcenet.com/states/oklahoma/common_law_marriage_in_oklahoma
states that recognize a common law marriage require that certain legal steps be taken. filing a tax return is not one of them. see a lawyer.
States that recognize common law marriage require that you both put yourself forward publicly as married in all matters.
Filing MFJ would be consistent with that.
You did not even say what filing status you submitted on your tax form(s).